Which nuclear shape generates the strongest attraction on a relativistic electron? An open problem in relativistic quantum mechanics

Autor:	Esteban, Maria J., Lewin, Mathieu, Séré, Eric
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics Mathematics - Spectral Theory
Zdroj:	In: Morel, JM., Teissier, B. (eds) Mathematics Going Forward, LNM 2313 (2023), pp. 487--497
Druh dokumentu:	Working Paper
DOI:	10.1007/978-3-031-12244-6_34
Popis:	In this article we formulate several conjectures concerning the lowest eigenvalue of a Dirac operator with an external electrostatic potential. The latter describes a relativistic quantum electron moving in the field of some (pointwise or extended) nuclei. The main question we ask is whether the eigenvalue is minimal when the nuclear charge is concentrated at one single point. This well-known property in nonrelativistic quantum mechanics has escaped all attempts of proof in the relativistic case. Comment: Mathematics Going Forward, In press
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.13484 Zobrazit plný text záznamu View this record from Arxiv